Divisibility Rules and Factors Worksheet

Quantitative aptitude lesson 3: Divisibility and factors · Set 183 · 40 questions

The method (Rules and powers): By 3 or 9: the digit sum divides by 3 or 9. By 4: the last two digits. By 8: the last three digits. By 6: even and divisible by 3. By 11: the sums of alternate digits are equal or differ by 11. Number of factors: write n = p^a × q^b …, then the count is (a + 1) × (b + 1) × …. To make n divisible by d: divide, then add (d − remainder) or take away the remainder.

1. 1.How many factors does 86 have?
2. 2.What is the smallest number you must add to 259 so that it divides exactly by 6?
3. 3.What is the smallest number you must add to 824 so that it divides exactly by 3?
4. 4.What is the smallest number you must take away from 106 so that it divides exactly by 6?
5. 5.What is the smallest number you must add to 751 so that it divides exactly by 4?
6. 6.What is the smallest number you must add to 959 so that it divides exactly by 4?
7. 7.How many factors does 67 have?
8. 8.Which of these numbers divides exactly by 11? (a) 6672 (b) 1124 (c) 5321 (d) 3982
9. 9.Which of these numbers divides exactly by 9? (a) 1716 (b) 2515 (c) 1962 (d) 4006
10. 10.How many factors does 62 have?
11. 11.Which of these numbers divides exactly by 11? (a) 2356 (b) 7150 (c) 6838 (d) 7055
12. 12.What is the smallest number you must take away from 406 so that it divides exactly by 12?
13. 13.How many factors does 91 have?
14. 14.Which of these numbers divides exactly by 9? (a) 5395 (b) 1010 (c) 1242 (d) 1676
15. 15.What is the smallest number you must add to 201 so that it divides exactly by 11?
16. 16.How many factors does 65 have?
17. 17.What is the smallest number you must add to 492 so that it divides exactly by 8?
18. 18.What is the smallest number you must take away from 198 so that it divides exactly by 4?
19. 19.What is the smallest number you must add to 307 so that it divides exactly by 6?
20. 20.How many factors does 28 have?
21. 21.What is the smallest number you must take away from 815 so that it divides exactly by 9?
22. 22.How many factors does 59 have?
23. 23.What is the smallest number you must take away from 977 so that it divides exactly by 7?
24. 24.Which of these numbers divides exactly by 8? (a) 5367 (b) 6161 (c) 6784 (d) 8563
25. 25.What is the smallest number you must take away from 929 so that it divides exactly by 9?
26. 26.What is the smallest number you must take away from 992 so that it divides exactly by 11?
27. 27.How many factors does 48 have?
28. 28.Which of these numbers divides exactly by 4? (a) 2850 (b) 2688 (c) 8549 (d) 1486
29. 29.Which of these numbers divides exactly by 8? (a) 2687 (b) 3575 (c) 3296 (d) 3093
30. 30.What is the smallest number you must add to 483 so that it divides exactly by 6?
31. 31.How many factors does 16 have?
32. 32.What is the smallest number you must add to 988 so that it divides exactly by 9?
33. 33.What is the smallest number you must add to 555 so that it divides exactly by 6?
34. 34.Which of these numbers divides exactly by 4? (a) 9039 (b) 3338 (c) 8205 (d) 5704
35. 35.Which of these numbers divides exactly by 3? (a) 1447 (b) 8059 (c) 9827 (d) 2370
36. 36.How many factors does 19 have?
37. 37.Which of these numbers divides exactly by 8? (a) 8044 (b) 4379 (c) 7704 (d) 7927
38. 38.Which of these numbers divides exactly by 8? (a) 3186 (b) 9367 (c) 7224 (d) 2847
39. 39.How many factors does 71 have?
40. 40.What is the smallest number you must take away from 853 so that it divides exactly by 11?

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